We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in D dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We also discuss duality transformations that give different field theory representations of the same physical degrees of freedom, and discuss the example of gravit...

The Hull-Witten proof of the local gauge and Lorentz invariance of the Qmodel describing the propagation of the heterotic string in arbitrary background field is extended to higher orders in cy’. The modification of the transformation laws of the antisymmetric tensor field under these symmetries is discussed. Finally we point out the existence of an anomaly in the naive N = f supersymmetry tran...

It has been almost one hundred years since Einstein formulated his special theory of relativity in 1905. He showed that the basic space-time symmetry is dictated by the Lorentz group. It is shown that this group of Lorentz transformations is not only applicable to special relativity, but also constitutes the scientific language for optical sciences. It is noted that coherent and squeezed states...

It has been almost 100 years since Einstein formulated his special theory of relativity in 1905. He showed that the basic space–time symmetry is dictated by the Lorentz group. It is shown that this group of Lorentz transformations is not only applicable to special relativity, but also constitutes the scientific language for optical sciences. It is noted that coherent and squeezed states of ligh...

Abstract In special relativity, four-vectors, such as space–time, energy–momentum and electromagnetic potential vectors, follow the Lorentz transformation. The transformations of space–time vectors have been tested by time dilation rest mass energy experiments, respectively. However, transformation potentials has never directly demonstrated in experiments due to limitations diagnostics. Here we...

We complete a metric-free axiomatic framework for electrodynamics by introducing the appropriate energy-momentum current Σα of the electromagnetic field. We start from the Lorentz force density and motivate the form of Σα. Then we postulate it (fourth axiom) and discuss its properties. In particular, it is found that Σα is traceless and invariant under an electric-magnetic reciprocity transform...

The Inönü-Wigner contraction is applied to special relativity and the little groups of the Lorentz group. If the O(3) symmetry group for massive particle is boosted to an infinite-momentum frame, it becomes contracted to a combination of the cylindrical group and the two-dimensional Euclidean group. The Euclidean component becomes the Lorentz condition applicable to the electromagnetic four-pot...

We propose a new version of the superfield action for a closed D = 10, N = 1 superstring where the Lorentz harmonics are used as auxiliary superfields. The incorporation of Lorentz harmonics into the superfield action makes possible to obtain superfield constraints of the induced worldsheet supergravity as equations of motion. Moreover, it becomes evident that a so-called ’Wess-Zumino part’ of ...

Hitherto, we have focussed on applications of quantum mechanics to free particles or particles confined by scalar potentials. In the following, we will address the influence of a magnetic field on a charged particle. Classically, the force on a charged particle in an electric and magnetic field is specified by the Lorentz force law: Hendrik Antoon Lorentz 18531928 A Dutch physicist who shared t...